API 520 Formulas & Engineering Reference
| Case | Equation |
|---|---|
| Critical pressure ratio | rc = (2/(k+1))k/(k−1) |
| Gas, critical flow | A = W / (C·Kd·P₁·Kb·Kc) · √(T·Z/M) |
| Coefficient C | C = 0.03948·√(k·(2/(k+1))(k+1)/(k−1)) |
| Gas, subcritical | A = 17.9·W / (F₂·Kd·Kc) · √(Z·T/(M·P₁·(P₁−P₂))) |
| Subcritical factor | F₂ = √( (k/(k−1))·r2/k·(1−r(k−1)/k)/(1−r) ) |
| Liquid (certified) | A = 11.78·Q / (Kd·Kw·Kc·Kv) · √(G/(P₁−P₂)) |
| Relieving pressure | P₁ = Pset·(1 + overpressure) + Patm |
A = required orifice area (mm²), W = mass flow (kg/h), Q = liquid flow (L/min), P₁ = relieving pressure (kPa abs), P₂ = backpressure (kPa abs), T = relieving temperature (K), M = molecular weight, Z = compressibility, k = Cp/Cv, G = specific gravity. Kd = discharge coefficient, Kb/Kw = backpressure corrections (balanced bellows), Kc = 0.9 with an upstream rupture disc.
Why sizing uses relieving pressure, not set pressure
A relief valve doesn't pass its full capacity the instant it cracks open. The code allows the pressure to rise a further 10% (accumulation) while the valve strokes fully open — so the flow calculation is done at set + overpressure, in absolute terms. Using set pressure alone would oversize the valve slightly, which sounds safe but a grossly oversized PSV chatters: it slams open, dumps pressure, slams shut, and destroys its own seat.
Critical vs subcritical flow
Squeeze gas through a nozzle and its velocity at the throat rises until it hits the speed of sound — after that, lowering the downstream pressure changes nothing upstream. That's critical (choked) flow, and it's the normal regime for gas relief because relief pressures are usually well above twice the header pressure. Only when the backpressure is high relative to relieving pressure does the flow go subcritical and the F₂ correction appear.
Why backpressure decides the valve type
In a conventional spring valve, backpressure pushes on the disc from behind — it adds to the spring, so the valve opens late and its capacity falls. Above ~10% of set pressure that error is no longer acceptable. A balanced bellows isolates the disc from backpressure (up to ~50%); a pilot-operated valve uses process pressure itself to hold the seat and shrugs off even higher backpressure.
The discharge coefficient and compressibility factor
Kd corrects the ideal-nozzle equation for the real valve geometry — the 0.975 preliminary value reflects how close a good relief nozzle gets to ideal. Z corrects the ideal-gas density at relieving conditions; for LPG vapor near its saturation dome Z of 0.85–0.9 is typical, and assuming Z = 1 is conservative (it gives a larger required area).
| Letter | Area (in²) | Area (mm²) | Letter | Area (in²) | Area (mm²) |
|---|---|---|---|---|---|
| D | 0.110 | 71 | L | 2.853 | 1841 |
| E | 0.196 | 126 | M | 3.60 | 2323 |
| F | 0.307 | 198 | N | 4.34 | 2800 |
| G | 0.503 | 325 | P | 6.38 | 4116 |
| H | 0.785 | 506 | Q | 11.05 | 7129 |
| J | 1.287 | 830 | R | 16.0 | 10323 |
| K | 1.838 | 1186 | T | 26.0 | 16774 |
10% for a single valve on a non-fire case, 16% when multiple valves share the load, 21% for the external fire case — all per ASME VIII UG-125. The fire case usually sets its own separate sizing scenario.
From the governing relief scenario per API 521 — blocked outlet, fire, control valve failure, tube rupture, thermal expansion. Size for the scenario requiring the largest orifice. The LPG tank calculator estimates the fire-case vapor load for storage vessels.
API 520 Part II limits non-recoverable inlet line loss to 3% of set pressure — more and the valve chatters. Keep the inlet line short and at least the valve inlet size. Check it as a separate hydraulic calculation at rated flow.
It's the sizing basis. Final selection uses the manufacturer's certified discharge coefficient and actual orifice area, plus inlet/outlet flange ratings per API 526 and material selection for the service.